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Simplifying 0 = x3 + 8x2 + 16x Reorder the terms: 0 = 16x + 8x2 + x3 Solving 0 = 16x + 8x2 + x3 Solving for variable 'x'. Remove the zero: -16x + -8x2 + -1x3 = 16x + 8x2 + x3 + -16x + -8x2 + -1x3 Reorder the terms: -16x + -8x2 + -1x3 = 16x + -16x + 8x2 + -8x2 + x3 + -1x3 Combine like terms: 16x + -16x = 0 -16x + -8x2 + -1x3 = 0 + 8x2 + -8x2 + x3 + -1x3 -16x + -8x2 + -1x3 = 8x2 + -8x2 + x3 + -1x3 Combine like terms: 8x2 + -8x2 = 0 -16x + -8x2 + -1x3 = 0 + x3 + -1x3 -16x + -8x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -16x + -8x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(16 + 8x + x2) = 0 Factor a trinomial. -1x((4 + x)(4 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0, -4, -4}
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